If you are not feeling well, you shouldn’t ride unless you have to.
When you feel sick, you are not at the top of your game, and you will not be as alert as you should be. You tend to be more focused on how bad you feel instead of concentrating on your riding skills. Your reflexes will be slower and your judgement may not be the clearest. You will be uncomfortable.
In all seriousness, it would be better to not ride your motorcycle. If you are sick, it can be like you are drunk and that is not a good way to ride. Also, many over the counter cold medicines contain alcohol. Most of these cold remedies make you sleepy.
Plus, for those that wear a full-face helmet, coughing or sneezing in a helmet is not any fun, and can be messy.